Yes, they would see (practically) the same constellations along the band of sky they can both see. I assume this is the area you are talking about.
Otherwise, this is a trivial question: they would see different constellations outside of the swath of sky they share because there is a (another assumption!) sight-blocking planet between the two viewpoints. Since the internet has its fair share of pendants who take joy in pointing out the obvious, I ought to include this for completeness.
How Far Until They're Different?
It depends. How far away are the stars? Are any visibly close to each other? How much movement in stars' position qualifies as "different?"
There a phenomena called "parallax." This is the driving factor for change in constellations in this question. Astronomers use this (and the Earth's yearly trip around the sun) to calculate distances of far away stars. Wikipedia informes us that heliocentrism was argued against because the parallax effect wasn't particularly observable at the time. This is, of course, no longer the case!
We could have stars easily disappear if they are (visually) close to another. However, for an observer on a non-megastructure planet (like Earth!) this isn't likely to happen. You can play with some numbers to figure things out a situation which works...
Consider, however, the sky as seen from our nearest star Alpha Centauri. Astronomers have calculated that the sky looks nearly the same at 4.37 light years away!
The take away here is that, for most sizes of things we consider terrestrial planets, even if it is disk-shaped, these two observers will see the same constellations. They would need to be radically far away to see anything different. (With the caveat of "while looking at the same section of sky.")